Both parametric and non-parametric approaches to time series analysis have advantages and disadvantages. Parametric methods, although powerful and widely used, can yield inconsistent results due to the oversimplification of the observed phenomena, they require the setting of arbitrary constants for their creation and refinement, and, although these constants relate to assumptions about the observed systems, it can lead to erroneous results when treating a very complex problem with a sizable list of unknowns. Their non-parametric counterparts, instead, are more widely applicable but present a higher detrimental sensitivity to noise and low density in the data. For the case of approximately periodic phenomena, such as human actigraphic time series, parametric methods are widely used and concepts such as acrophase are staple in chronobiology; in this work we present a non-parametric method of analysis of actigraphic time series from insomniac patients and healthy age-matched controls, the method is fully data-driven, reproduces previous results in the context of sleep-onset delay and, crucially, extends the concept of acrophase not only to circadian but also for ultradian spectral components.

This is the set of code in matlab used to calculate fourier phases and amplitudes, probability distribution of motion, and to generate the corresponding figures in pdf format

a) Data files should exist in the same folder as code, otherwise, specifiy/modify main code

b) Import all data files in matlab to save per-condition MAT files with obtained information